Numerical Simulation of the Stochastic Neural Field Equation with Delay

The Neural Field Equations (NFE) are used to model the synaptic interactions between neurons in a continuous neural network, called a neural eld. This kind of integro-di erential equations proved to be an useful tool to describe the spatiotemporal neural activity from a macroscopic point of view, allowing the study of a wide variety of neurobiological phenomena, such as the sensory stimuli processing. The present article aims to study the e ects of additive noise in one- and twodimensional neuronal elds, while taking into account nite axonal velocity and external stimulus. A Galerkin-type method is presented, which applies Fast Fourier Transforms to optimise the computational e ort required to solve these equations. The explicit Euler-Maruyama scheme is implemented to obtain the stochastic numerical solution. A published numerical solver written in Julia is used to simulate the neural elds in study.